NEET 2020 Physics Question 143 Solution

The gravitational force (weight) acting on a mass $$m$$ at the surface of the Earth (radius $$R$$, mass $$M$$) is: $$W = \frac{G M m}{R^2} = 72\text{ N}$$ At a height $$h$$ above the surface, the distance from the center of mass of the Earth is $$r = R + h$$. The gravitational force is: $$W' = \frac{G M m}{(R + h)^2} = W \left(\frac{R}{R + h}\right)^2$$

The linear approximation $$g' = g(1 - 2h/R)$$ is valid ONLY when $$h \ll R$$ (typically $$h < 5\% \text{ of } R$$). Here, $$h = R/2$$ is comparable to the radius of Earth, making the exact inverse-square formula mandatory.

$$R + h = R + \frac{R}{2} = \frac{3}{2}R$$ $$\frac{R}{R + h} = \frac{R}{\frac{3}{2}R} = \frac{2}{3}$$

$$W' = 72 \times \left(\frac{2}{3}\right)^2 = 72 \times \frac{4}{9}$$ Notice that $$72 / 9 = 8$$: $$W' = 8 \times 4 = 32\text{ N}$$ This confirms Option (2).